In this exercise we show how to compute the concentration of uranium in an ore from the

Chapter 1, Problem 1

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In this exercise we show how to compute the concentration of uranium in an ore from the dpm/(g of Pb) of the lead-210 in the ore. (a) The half-life of uranium-238 is 4.51 x lo9 years. Since this half-life is so large, we may assume that the amount of uranium in the ore is constant over a period of two to three hundred years. Let N (t) denote the number of atoms of 238U per gram of ordinary lead in the ore at time t. Since the lead-210 is in radioactive equilibrium with the uranium-238 in the ore, we know that dN/dt = -AN= - 100 dpm/g of Pb at time t,. Show that there are 3.42 x 10" atoms of uranium-238 per gram of ordinary lead in the ore at time 1,. (Hint: 1 year - 525,600 minutes.) (b) Using the fact that one mole of uranium-238 weighs 238 grams, and that there are 6.02 x atoms in a mole, show that the.concentration of uranium in the ore is approximately 0.014 percent.